Scaling Recipes and Quantities by Ratio
Scaling recipes and quantities by ratio means increasing or decreasing every quantity in a recipe or list of linked amounts by the same scale factor, so the ratio between them stays the same. This is a common real-world context on 11+ papers, building on direct proportion by requiring several linked amounts to be scaled together consistently, rather than a single pair of quantities.
Method
- Identify which quantity in the recipe or list you are told the new value for, and which original quantity it corresponds to.
- Find the scale factor by dividing the new amount by the original amount for that one quantity.
- Multiply every other quantity in the recipe or list by the same scale factor, so everything stays in proportion.
- If the scale factor is not a whole number, keep it as a fraction or decimal through your working rather than rounding early, to avoid errors building up.
- Convert any units so they match before scaling, since scaling mismatched units, such as grams and kilograms, gives a wrong answer.
- Check your scaled quantities keep the same ratio as the originals by simplifying both sets and comparing them.
Worked example
A pancake recipe for 8 pancakes uses 200 g of flour, 2 eggs and 300 ml of milk. Scale the recipe to make 20 pancakes.
- Find the scale factor by dividing the new number of pancakes by the original: 20 / 8 = 2.5.
- Scale the flour: 200 x 2.5 = 500 g.
- Scale the eggs: 2 x 2.5 = 5 eggs.
- Scale the milk: 300 x 2.5 = 750 ml.
- Final answer: 500 g flour, 5 eggs and 750 ml milk.
Practice questions
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Q1A recipe for 4 people uses 120 g of rice. Scale it for 6 people.Show answer
Answer: 180 g (scale factor 1.5, and 120 x 1.5 = 180)
Q2A paint mix uses blue and white paint in the ratio 2 : 3. If 10 litres of blue paint is used, how much white paint is needed?Show answer
Answer: 15 litres (one part = 10 / 2 = 5 litres, and 3 x 5 = 15)
Q3A recipe uses 3 eggs for every 250 g of flour. How many eggs are needed for 750 g of flour?Show answer
Answer: 9 eggs (scale factor 750 / 250 = 3, and 3 x 3 = 9)
Q4A squash drink is mixed in the ratio 1 : 4 (squash to water). How much water is needed for 50 ml of squash?Show answer
Answer: 200 ml (one part = 50 ml, and 4 x 50 = 200)
Q5A cake recipe for 12 people uses 360 g of sugar. How much sugar is needed to make the recipe for 3 people?Show answer
Answer: 90 g (scale factor 3 / 12 = 0.25, and 360 x 0.25 = 90)
Q6A recipe requires 2 eggs, 100 g of butter and 150 g of sugar to serve 5 people. Find the amount of butter needed to serve 15 people.Show answer
Answer: 300 g (scale factor 15 / 5 = 3, and 100 x 3 = 300)
Q7Explain why it is important to scale every ingredient in a recipe by the same scale factor.Show answer
Answer: The scale factor keeps the ratio between the ingredients exactly the same as the original recipe; if only some ingredients were scaled, the balance of the mixture would change and the recipe would not behave or taste as intended.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A fruit punch recipe for 10 people uses 400 ml of orange juice, 200 ml of lemonade and 150 g of frozen berries. Scale the recipe to serve 25 people.
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A bread recipe for one loaf uses flour, water and yeast in the ratio 500 : 300 : 8 (grams : millilitres : grams). A baker wants to make loaves using 3000 g of flour. (a) Find the scale factor compared to the original recipe. (b) Work out how much water is needed. (c) Work out how much yeast is needed.
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Free printable worksheet
Want more practice on paper? Download the scaling recipes and quantities by ratio worksheet pack - 8 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 7 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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